**Papers Published**

- with H. Edelsbrunner.,
*Jacobi sets of multiple Morse functions.*, Foundations of Computational Mathematics, Minneapolis, eds. F. Cucker, R. DeVore, P. Olver and E. Sueli, Cambridge Univ. Press, England, (2002), pp. 37-57

(last updated on 2004/12/15)**Abstract:**

The Jacobi set of two Morse functions defined on a common d-manifold is the set of critical points of the restrictions of one function to the level sets of the other function. Equivalently, it is the set of points where the gradients of the functions are parallel. For a generic pair of Morse functions, the Jacobi set is a smoothly embedded 1-manifold. We give a polynomial-time algorithm that computes the piecewise linear analog of the Jacobi set for functions specified at the vertices of a triangulation, and we generalize all results to more than two but at most d Morse functions.